This is an interesting question as I personally am not too sure that the character of Ariel is shown to develop during the course of this brilliant play. In fact, if we compare him to Caliban, we could argue that he is not actually that developed at all as a character and stays the same, remaining a static character, throughout the play. He starts off as a character who appears to rebel against the servitude that has been forced against him. However, these complaints are belied by the evident joy that Ariel takes in fulfilling his duties. Note, for example, what he says to Prospero in Act I scene 2:

All hail, great master! grave sir, hail! I come

To answer thy best pleasure; be't to fly,

To swim, to dive in the fire, to ride

On the curl'd clouds, to thy strong bidding task

Ariel and all his quality.

In addition, he shows himself to be a faithful hardworking servant who does all that is asked of him without trying to deceive his master: "Remember I have done thee worthy service; / Told thee no lies, made no mistakings, serv'd / Without grudge or grumblings." In this sense he acts as a foil to Caliban, who definitely does not serve Prospero in this way. These aspects of Ariel's character remain constant throughout the play. Whilst he certainly is enslaved by Prospero, at the same time he delights in his work and enjoys using his powers to trick, deceive and manipulate the humans on the island. Therefore, I don't actually think we see much development in his character.